I've been recording 4k signal from an A7s/GH4 to the Video Assist 4k and recently started dabbling with using the HDMI out for 'video village' while recording on the monitor.

Ideally, I'd like to start transmitting wirelessly, through the VA HDMI out, but it's going to be more expensive if I have to transmit the clean 4k signal. I was wondering if there's a way to have the VA downscale the HDMI out to 1080p while still recording 4K?

The SDI and HDMI outputs are not a loop output, they are a post process output from thr recorder, so there will be a slight delay. The VA4K does not downscale the signal, and the outputs will be at the same resolution as the input. That said, you can Use a UHD to HD down Converter to get a HD signal to transmit. Cheers